Listen carefully
Make it your starting point to understand them rather than a need to win the argument or make them behave. Listen to the tune, not the words. So instead of hearing 'I hate you! Why don't you leave me alone?' you hear, 'I'm really upset, I'm trying to manage on my own and it feels like you don't trust me!'.
By trying to understand what is really going on beneath what they are saying, you can help them work out what they are really feeling, and what it is they need. Just the act of listening to them helps to lower the emotional temperature and can bring them back into balance. It can also help to name what you think your child might be feeling, for example, in the face of apparent screaming anger, to say, 'You sound really frustrated, or 'It sounds as if you're feeling scared.' By naming the emotion, you can help your teenager work out what they want or need.